Question: Solve for $f$. $-f+2+4f=8-3f$ $f =$
Answer: We need to manipulate the equation to get $ f $ by itself. $\begin{aligned} -f+2+4f&=8-3f\\\\ 2+3f&=8-3f &&\gray{\text{Combine like terms.}}\\\\ 2+3f {+3f} &= 8-3f{+3f} &&\gray{\text{Add 3f to each side.}}\\\\ 6f+2&=8 &&\gray{\text{Combine like terms.}}\\\\ 6f+2{-2} &= 8{-2} &&\gray{\text{Subtract 2 from each side.}}\\\\ 6f &=6 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{6f}{{6}} &= \dfrac{6}{{6}} &&\gray{\text{Divide each side by 6.}}\\\\ f &= {1} &&\gray{\text{Simplify.}} \end{aligned}$ The answer: $f = { 1 }~~~~~~~~$ [Let's check our work!]